An experiment measuring the percent shrinkage on drying of 50 clay specimens produced the following data:
|
18.2
|
21.2
|
23.1
|
18.5
|
15.6
|
|
20.8
|
19.4
|
15.4
|
21.2
|
13.4
|
|
16.4
|
18.7
|
18.2
|
19.6
|
14.3
|
|
16.6
|
24.0
|
17.6
|
17.8
|
20.2
|
|
17.4
|
23.6
|
17.5
|
20.3
|
16.6
|
|
19.3
|
18.5
|
19.3
|
21.2
|
13.9
|
|
20.5
|
19.0
|
17.6
|
22.3
|
18.4
|
|
21.2
|
20.4
|
21.4
|
20.3
|
20.1
|
|
19.6
|
20.6
|
14.8
|
19.7
|
20.5
|
|
18.0
|
20.8
|
15.8
|
23.1
|
17.0
|
(a) Draw a stem and leaf plot of these data.
(b) Compute the sample mean, median, and mode.
(c) Compute the sample variance.
(d) Group the data into class intervals of size 1 percent starting with the value 13.0, and draw the resulting histogram.
(e) For the grouped data acting as if each of the data points in an interval was actually located at the midpoint of that interval, compute the sample mean and sample variance and compare this with the results obtained in parts (b) and (c). Why do they differ?